Question: At the beginning of the season, MacDonald had to remove $5$ orange trees from his farm. Each of the remaining trees produced $210$ oranges for a total harvest of $41790$ oranges. Write an equation to determine the initial number of orange trees $(t)$ on MacDonald's farm. Find the initial number of orange trees on MacDonald's farm.
Answer: Let $t$ be the initial number of trees. MacDonald now has $t-5$ trees and each one produced $210$ oranges this harvest. The total number of oranges produced is $210(t-5)$. Since the trees produced a total of $41790$ oranges, let's set this equal to $41790$ : $ 210(t-5)=41{,}790$ Now, let's solve the equation to find the initial number of trees $(t)$. $\begin{aligned}210(t-5)&=41790\\&\\ \dfrac{210(t-5)}{{210}}&=\dfrac{41790}{{210}}&&\text{divide both sides by ${210}$}\\ \\ t-5&=199\\ \\ t-{5}{+5}&=199{+5}&&{\text{add }} {5} \text{ to both sides}\\ \\ t&=204\end{aligned}$ The equation is $210(t-5)=41790.$ MacDonald's farm initially had $204$ orange trees.